简介:
简介:§1.IntroductionIn[1],R.SchoenandS.T.Yanusedharmonicmaptostudythetopologyofanon-compactcompletestablehypersurfaceinamanifoldofnon-negativecurvature.Essentiallythemethodistoprovefirstthenonexistenceofsomekindofnonconstantharmonicmapandthentodrawtherelativeconclusionsconcerningthetopology.Suchnonexistencetheoremshavebeenobtainedin[3]and[4]incaseswheretheconcernedmanifoldsarecompact.Theaimofthispaperistostudythenon-compactcompletecase.Ourmainresultscanbestatedasfollows.
简介:ThispaperstudiestheuniquenessoftheharmonicmapsfromRnintoSn-1.Atfirstitisprovedthatthemapψ(x)=x|x|:Bn→Sn-1istheuniqueenergyminimizingharmonicmap.ThentheuniquenessoftheharmonicmapswithidentityboundaryvaluefromBntoSn-1follows.
简介:LetG(m,s,t,λ)bethenumberofwaysofλ-coloringalltherootednonseparableouterplanarmapswhicharesimpleandhavetheedgenumberm,thevalencysoftheroot-face,andthevalencytoftheroot-vertex.Thechromaticenumeratingfunctiong(x,y,z;λ.)=G(m,s,t;λ)x~my~sz~tisdetermined.Meanwhile,anumberofexplicitformulaeforenumeratingthiskindofmapsingeneralcaseandinLipartitecaseareprovided.
简介:Thisnoteshowsthatthenumberofrootedcubicplanarmaps(loopsandmulti-edgesareallowed)with2n-3non-root-vertices,n≥3,is
简介:<正>AconjugaeybetweenC1+αΣ-hyperboliccirclecoveringmapsisC1+αifithasapositivederivativeonsomepointintheΣ-set.
简介:Inthispaper,thenumberofcombinatoriallydistinctrootednonseparableouterplanarmapswithmedgesandthevalencyoftheroot-facebeingnisfoundtobe(m-1)!(m-2)!:(n-1)!(n-2)!(m-n)!(m-n+1)!and,thenumberofrootednonseparableouterplanarmapswithmedgesisalsodeterminedtobe(2m-2)!:(m-1)!m!,whichisjustthenumberofdistinctrootedplanetreeswithm-1edges.
简介:Inthispaper,wediscusstherank-l-preservinglinearmapsonnestalgebrasofHilbertspaceoperators.WeobtainseveralcharacterizationsofsuchlinearmapsandapplythemtoshowthataweaklycontinuouslinearhijectiononanatomicnestalgebraisidempotentpreservingifandonlyifitisaJordanhomomorphism,andinturn,ifandonlyifitisanautomorphismorananti-automorphism.
简介:在里面[加拿大数学。公牛。22,pp。513515,1979],作者延长了一有趣(最好的近似)Ky扇子的定理[看见定理2,数学。Z。112,pp。234240]到在一个Banach空格在一个关上的球定义并且在一个Hilbert空格在一个关上的凸的子集上定义的压缩地图。在里面[J。近似理论52,pp。141148,1988],作者和日元进一步在一个Hilbert空格扩大了它到1-set-contractive地图。在这份报纸,我们将探讨几个相关问题。首先,我们扩大林,日元为1-set-contractive地图,但是到结果满足更弱的状况,它允许我们包括概括收缩地图。第二,我们让路为nonexpansive地图构造最好的近似(不仅仅存在结果)。第三,我们给上的条件最好的近似{un|n=1,2,}收缩的一个序列{fn|n=1,2,}将收敛到收缩f的最好的近似u。第四,为nonexpansive地图的普通最好的近似定理被证明。到为弱里面的地图和其它的固定的点定理的应用为所有那些四个话题被给。
简介:BymeansofthetheoryofharmonicmapsintotheunitarygroupU(N),theauthorsstudyharmonicmapsintothesymplecticgroupSp(N).Thesymplecticunitonandsymplecticex-tendedunitonareintroduced.ThemethodofthesymplecticBacklundtransformationandtheDarbouxtransformationisusedtoconstructnewsymplecticunitonsfromaknownone.
简介:LetUn(C),GLn(C)andMn(C)bethen-degreeunitarygroup,thenn-degreegenerallineargroupandthesemigroupsofalln×nmatricesovercomplexnumberfieldCrespec-tively.Hochwaldin[1]showedthatiff:Un(C)→Mn(C)isaspectrum-preservingmulti-plicativemap,thenthereexistsamatrixRinGLn(C)suchthatf(A)=R-1ARforallA∈